复变函数法计算圆形盾构隧道周边土体位移

盾构隧道开挖引起隧道周围土体应力及位移的改变,是工程界长期关注的重要课题.将半无限空间弹性单圆孔洞问题,映射为复平面上定值圆环问题,并利用隧道孔洞边界土体与衬砌之间空间位置及协调变形关系,给出了圆形盾构隧道周边土体位移的复变函数解,采用Matlab软件实现算法.结果表明:复变函数解析法计算得到的隧道地表沉降曲线与实测曲...     

疫情下《复变函数与积分变换》课程弹性教学模式探索

根据弹性教学的背景和意义,针对疫情期间线上教学面临的问题,将弹性教学理念引入复变函数与积分变换课程教学中。探讨弹性教学在本课程中具体实施步骤及关键点。为疫情期间线上教学提供参考,具有一定的实际意义。     

弹性接触变形问题的数值解及其应用

通过对弹性空间问题基本方程的简化求解，可计算任意分布力作用下的弹性接触变形问题。     

弹性接触变形问题的数值解及其应用

通过对弹性半空间问题基本方程的简化求解，可计算任意分布力作用下的弹性接触变形问题。     

深埋马蹄形隧道开挖围岩应力与位移的复变函数解

利用复变函数解法中的柯西积分法,求解工程中常用的单心圆仰拱马蹄形隧道在弹性半空间内任意一点处的应力值和位移值解析解表达式。由于是深埋隧道,且埋深与孔径之比较大,故不考虑重力梯度影响,直接把重力作用化为无限远处作用有 P1、P2的外载;求解出马蹄形隧道孔洞在弹性半空间内任意一点处的应力值和位移值解析解表达式。结合典型断面,利用三维有限元分析软件M ADIS/G T S建立二维平面应变模型,对理论推导单心圆马蹄形隧道在弹性平面内的解析解公式进行验证。分析表明,有限元结果和解析解结果有较好的吻合性,证明了新方法的准确性,针对深埋马蹄形隧道开挖工程,可以快捷地评估围岩应力状态及位移变形。     

基于复变理论的城门洞型隧洞围岩黏弹性位移解析解（研究生论坛）

围岩蠕变特性是影响隧洞长期稳定性的主要因素,目前对黏弹性位移仅得到圆形、椭圆形和矩形等简单边界的解析表达式,而对城门洞型隧洞,则尚未提出较精确的黏弹性位移计算式。基于任意边界的围岩弹性位移的计算过程,运用复变函数理论,根据实际情况简化计算模型,推导了城门洞型隧洞围岩边界位移的弹性解析解,再根据弹性-黏弹性对应原理,通过Laplace变换及其逆变换进一步得到了城门洞型隧洞边界位移的黏弹性解析解。结合某软岩隧洞工程,开展解析解、弹性有限元及FLAC3D流变分析,计算表明：三种计算方法洞室边界黏弹性变形规律基本相似,初始弹性变形吻合较好,且黏性变形的演变规律与数值分析及现场实测结果基本一致,表明应用文中方法的实用性和可靠性。     

弹性支承桩受迫振动问题广义函数解及应用

本文首先利用广义函数（狄拉克δ－函数）建立了桩端为弹性支承时,考虑桩侧土作用,桩顶受稳态正弦激振条件下,基桩纵向振动问题的定解问题,随后求得了其解析解,接着由迭加原理求得了瞬态半正弦激振条件下的解。最后,将瞬态激振条件下得到的理论曲线与反射波法测得的实际曲线进行了拟合对比,结果表明两者较为一致。     

船体结构非圆孔口问题的复变函数解

针对船体焊接结构上甲板大开口边缘,舱壁开口边缘的应力集中现象严重影响船体强度这一问题,根据弹性力学基本理论,引入保角变换技术,以无限大平板一般形状孔口为算例,给出了适合数值计算的复变函数解法.并且按照这一方法编制了相应的计算程序,具体计算了船体结构和工程中常见的曲线孔口———六角形孔和腰圆孔在均匀拉伸和纯弯曲两种情况下的孔边最大应力、应力分布及腰圆孔长宽比对应力集中问题的影响,并对比了板宽变化对孔口应力的影响.实算结果与有关文献及边界元法的计算结果十分吻合.     

层状土中考虑剪切变形的单桩水平振动解析解

针对桩基水平振动分析问题，建立了能够同时考虑桩体弯曲和剪切变形的桩土计算模型.采用与频率相关的刚度系数和阻尼系数来模拟土对桩的动反力，简化桩体为Timoshenko梁，得到了层状黏弹性地基中能同时考虑桩体弯曲和剪切变形的单桩的水平振动解析解.研究了桩土模量比、桩体长径比、地基成层性以及激振频率对桩基动力响应的影响.并且在给定桩土参数的情况下，把同时考虑桩体弯曲和剪切变形的解析解与只考虑弯曲变形的解进行了比较.结果表明，忽略桩体水平振动时的剪切变形可能会带来较大的误差.     

弹性曲梁静态大变形数学模型及其数值解

基于Kirchhoff直法线假设，采用考虑轴线可伸长的几何非线性理论，建立了弹性曲梁在任意荷载（保守和非保守）作用大变形问题的控制方程，其中包含轴线弧长，位移，转角，内力等7个独立未知函数，通过引进变形后的孤长为未知函数后，问题的求解区间则固定不变，该模型不仅考虑了轴线可伸长，同时精确地考虑了轴线的初始曲率对变形的影响，反映了轴向变形与弯曲变形的相互耦合效应，作为应用，用打靶法具体计算了一端固定另一端自由，沿轴线作用均布切向随动载荷的半圆形曲梁的非线性平面弯曲问题，给出了随载荷参数大范围变化的平衡路径曲线及平衡构形。     

Effects of liquefaction-induced large lateral ground deformation on pile foundations

The pile-soil system interaction computational model in liquefaction-induced lateral spreading ground was established by the finite difference numerical method.Considering an elastic-plastic subgrade reaction method,numerical methods involving finite difference approach of pile in liquefaction-induced lateral spreading ground were derived and implemented into a finite difference program.Based on the monotonic loading tests on saturated sand after liquefaction,the liquefaction lateral deformation of the site where group piles are located was predicted.The effects of lateral ground deformation after liquefaction on a group of pile foundations were studied using the fmite difference program mentioned above,and the failure mechanism of group piles in liquefaction-induced lateral spreading ground was obtained.The applicability of the program was preliminarily verified.The results show that the bending moments at the interfaces between liquefied and non-liquefied soil layers are larger than those at the pile＇s top when the pile＇s top is embedded.The value of the additional static bending moment is larger than the peak dynamic bending moment during the earthquake,so in the pile foundation design,more than the superstructure＇s dynamics should be considered and the effect of lateral ground deformation on pile foundations cannot be neglected.     

浅埋矩形顶管求解的复变函数实践

同时考虑洞周边界与地表边界,采用复变函数法求解浅埋矩形顶管施工引起的土体应力场、位移场。根据黎曼存在定理、复变函数的三角插值理论,提出计算含矩形的半无限域到同心圆环域共形映射的计算方法。在此基础上,将边界条件等式两边都展成洛朗级数,采用幂级数解法求得了复应力函数的系数。从该解法与有限元解的对比来看,在大部分点处结果相差不大,误差在2%左右。结果表明:(1)提出的保角映射函数形式及系数的求解方法适用于浅埋矩形隧洞;(2)提出的复变函数解法具有步骤清晰、收敛快、操作简单等特点。     

Hazard development mechanism and deformation estimation of water solution mining area

1 INTRODUCTION Water solution mining-based mineral deposit belongs to the ancient landlocked evaporation of salt lake mineral deposits. The salty mineral products of mining area, such as verde salt, rock salt, glauberite, etc., mainly exist in the salty rock segment that is formed by the third sulphate sediment of group of new ditch. This rock segment consists of mudstone, anhydrite-included calcium Glauber’s salt rock, calcium Glauber’s salt rock of mudstone quality, verde salt and roc…     

Influences of pre-existing fracture on ground deformation induced by normal faulting in mixed ground conditions

Physical model tests have been conducted by various researchers to investigate fault rupture propagation and ground deformation induced by bedrock faulting. However, the effects of pre-existing fracture on ground deformation are not fully understood. In this work, six centrifuge tests are reported to investigate the influence of pre-existing fracture on ground deformation induced by normal faulting in sand, clay and nine-layered soil with interbedded sand and clay layers. Shear box tests were conducted to develop a filter paper technique, which was adopted in soil model preparation to simulate the effects of pre-existing fracture in centrifuge tests. Centrifuge test results show that ground deformation mechanism in clay, sand and nine-layered soil strata is classified as a stationary zone, a shearing zone and a rigid body zone. Inclination of the strain localization is governed by the dilatancy of soil material. Moreover, the pre-existing fracture provides a preferential path for ground deformation and results in a scarp at the ground surface in sand. On the contrary, fault ruptures are observed at the ground surface in clay and nine-layered soil strata.     

Vlasov板弯曲振动问题的位移通解

针对Vlasov板弯曲振动的定解方程 ,给出了一个形式简洁的位移通解 ,最后给出了几点简化结果     

Stress analytical solution for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform distributed pressure

The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common cases.Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given.The power series method of complex function is used.The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted.The distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0,45 and 90,are obtained.An example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials.In that way,stress concentration at the inner surface can be alleviated and the stress distribution is more uniform.This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.     

全空间上一类Kirchhoff型问题正基态解的存在性

在全空间上应用Nehari流形和集中紧性原理研究了如下一类Kirehhoff型问题:{-(a+b∫RN|▽u|2dx)▽u+u=Q(x)|u|p-2u,∈RN;u∈H1(RN),u＞0,x ∈RN,并证明了该问题至少存在一个正基态解.该结果补充了文献[1-4]关于正基态解的存在性结果.     

Predictive analysis of stress regime and possible squeezing deformation for super-long water conveyance tunnels in Pakistan

The prediction of the stress field of deep-buried tunnels is a fundamental problem for scientists and engineers. In this study, the authors put forward a systematic solution for this problem. Databases...